George Walford, Eric Stockton, Jim Addison: NIAT and MetaNIAT

Letter from Jim Addison

Sir,
Whenever I read IC I am always baffled by this obsession with NIAT. It’s all over the place. Obviously the criticism of this made by Nicolas Walter has not been understood, so I would like to add mine as well.

NIAT constitutes a paradox and as such cannot be used as a base for making meaningful statements. To solve the dilemma some more information is needed. One has to distinguish two different types of sentences which constitute two different types of language, i.e. the ‘object language’ and the ‘metalanguage.’ This is the method the logician Alfred Tarski used to demonstrate how paradoxes can be avoided. His correspondence theory is that if we are to talk about truth for the sentences of a particular language, then we need a more general language, the metalanguage, in which we can refer both to the sentences of the object language and to the facts with which those object-language sentences are intended to correspond.

Yours etc. Jim Addison

REPLY
Once more an attempted rejection of NIAT goes on to demonstrate unrecognised acceptance of it. The proposition, Nothing Is Absolutely True, amounts to nothing, and of course nothing cannot be used as a base for meaningful statements. Of course more information is needed; you can’t make meaningful statements about nothing. But neither can you make a meaningful statement that is absolutely true.

The suggestion that one can avoid tanglefoot logical difficulties by using the concept of metalanguage collapses at a touch. Introducing metalanguage our correspondent makes statements about it (e.g. that it is more general). In what language are those statements couched? By his own argument it has to be ‘meta’ to the metalanguage, a metametalanguage. And this statement we have just made about this metametalanguage must itself be in a metametametalanguage, and so on endlessly. If Tarski did avoid paradox, he did so only by falling into infinite regression.

Why this horror of paradox? It derives from the search for a simple, rigid, totally one-sided truth, an attempt to realise the Aristotelian abstraction of an X which shall not be, not to any extent or in any sense, also non-X. This search is limited to a single phase of ideological development, that of precision. The stages before this are more easy-going, the first responding to experience as it comes, without examination or analysis, the second submitting experience to principles but not seeking exactitude. And the stages which follow precision, at first in their practice and later in theory too, find the simple X, that is not also non-X, insufficient. These appear in politics as the reformist and revolutionary movements. Taking present society as their X they seek to change it into something else, thereby implying that it is, potentially, what it is not, that X is also non-X.

Accepting that simple, undivided identity appears only as an imaginary abstraction, that in concrete reality everything is this and that, we find the solution to Tarski’s problem. The rigid and artificial division between object-language and metalanguage softens, and every language becomes, potentially at least, both object- language and metalanguage. X is also non-X. Then the metalanguage, once we start to make statements about it, becomes itself an object-language. That infinite series arises only from the attempt to avoid the paradox that nothing is simply itself, that everything is also what it is not, a paradox that experience overwhemingly validates.

Letter from Eric Stockton

Sir,
With regard to NIAT, ‘nothing’ presumably means no claim as to fact, in which case I think you are in a semantic bind so far as the claim, NIAT is itself of an absolute nature. Is this question not the first cousin of the famous sheet of paper on one side of which is written: ‘The statement on the other side is true’ while on the other side is written: ‘The statement on the other side is false’.

Yours etc. Eric Stockton

REPLY
Yes, NIAT does make an absolute claim. But what is that claim? Nothing. NIAT claims that there is an absolute truth. But what is that truth? Nothing.

NIAT claims that nothing is absolutely true and in making that claim both proves its falsity (by providing an instance of absolute truth) and confirms its validity (by asserting the only absolute truth to be nothing).

NIAT is, like that sheet of paper, a paradox, and various people from Aristotle onward have tried to show that paradoxes don’t, or can’t, or at least ought not, exist. But they are still there, grinning at us. Russell’s theory of types, intended to eliminate them from serious thinking, actually rested on one, namely that you must never say: ‘You must never say.’ Or, as one philosopher has put it: ‘ Russell challenged the legitimacy of self-reference – of having thought think about itself. Examples of sentences that refer to themselves (where someone says he is currently lying, for example), to contradictions that should be avoided. So Russell jumps to a theory of types that declares that no logical expression can ever refer to itself. There is no way of talking about everything, since such talk would have to include itself in its subject-matter.

The problem with this solution to the paradox is that it violates its own rubric. The theory of types applies to all logical expressions. Since it is itself a logical expression, it violates its own ban on self-reference.’ [1]

Unless we are prepared to accept a no-go area in our understanding, we have to get to grips with paradox, and with NIAT as the absolute paradox.

‘In principle Communists did not condone mass murder, or even the radical deprivation of liberty. Hitler never said he was a humanist, but the Bolsheviks did, and this was their undoing.’ (G. M. Tamas TLS May 14, 15)